Digital SAT Math Formulas

Achieving a top score in the Math section of the Digital SAT requires a thorough command of essential math concepts and formulas. From algebraic structures to geometry principles, each topic is crafted to assess a student's analytical precision and problem-solving agility. A well-prepared student, fluent in these foundational formulas, can approach each question with clarity and confidence.

Here are 20 indispensable math formulas to support Digital SAT success. For families committed to excellence, our SAT tutoring programs offer a truly comprehensive approach, guiding students through every vital concept and formula with unmatched expertise. Join us to provide your student with an elite learning experience, designed to inspire and empower future academic success.

1. Slope-Intercept Form of a Line

The slope-intercept form of a linear equation is a way to represent a straight line on a graph.

• y is the dependent variable

• x is the independent variable

• m is the slope

• b is the y-intercept.

2. Slope Formula

The slope formula calculates the rate of change of a line.

• m is the slope of the line.

• (x₁, y₁) and (x₂, y₂) are two points on the line.

3. Slopes of Perpendicular Lines

The slopes of perpendicular lines are negative reciprocals of each other.

• m1 is the slope of one line.

• m2 is the slope of the perpendicular line.

4. Percentage Formula

The percentage formula calculates a portion or rate as a percentage of a whole.

• "Part" refers to the portion or the part of the whole that you're interested in.

• "Whole" refers to the total or the entire quantity.

• The result is multiplied by 100 to express it as a percentage.

5. Percentage Change

The percentage change formula calculates the relative change between two values as a percentage.

• "New Value" refers to the updated or current value.

• "Old Value" refers to the initial or previous value.

• The result is multiplied by 100 to express it as a percentage.

6. Simple Probability

• "Number of favorable outcomes" refers to the number of outcomes that satisfy the condition you're interested in.

• "Total number of outcomes" refers to the total number of possible outcomes in the sample space.

7. Distance-Rate-Time Formula

The distance-rate-time formula is a fundamental equation used to solve problems involving distance, rate (or speed), and time.

• "Distance" is the total distance traveled.

• "Rate" (or "Speed") represents the speed at which the object is moving.

• "Time" represents the duration of travel.

8. Quadratic Formula

The quadratic formula is a fundamental tool in algebra for solving quadratic equations. The quadratic formula provides the solutions for x (the values of x) that satisfy this equation.

9. Standard Form of a Quadratic

The standard form of a quadratic equation is a way of writing quadratic equations that simplifies their representation.

• a determines the direction and width of the parabola. (If a>0 the parabola opens upwards. If a<0, the parabola opens downwards.)

• b determines the horizontal shift (if any) of the parabola.

• c determines the vertical shift (if any) of the parabola. (Graphically, c is the y-intercept.)

10. Vertex Form of a Quadratic

The vertex form of a quadratic equation is an alternative way to represent a quadratic function.

• a is a non-zero constant that determines the direction and width of the parabola (positive a opens upwards, negative a opens downwards).

• (h,k) represents the coordinates of the vertex of the parabola. The vertex is the highest or lowest point on the graph of the quadratic function, depending on the value of a.

• h is the x-coordinate of the vertex.

• k is the y-coordinate of the vertex.

11. Factored Form of a Quadratic

The factored form of a quadratic equation is a way of expressing a quadratic equation as a product of linear factors.

12. Exponential Function

These are the values of x that make the quadratic equation equal to zero.

• a is the initial value or y-intercept.

• b is the growth or decay rate (decimal).

• If b>1, it signifies exponential growth.

• If 0<b<1, it indicates exponential decay.

13. Exponential Growth and Decay

Exponential growth and decay refer to the rapid increase or decrease of a quantity over time, following an exponential pattern.

• a is the initial amount or value at time .

• r is the growth or decay rate (decimal).

• x is time.

14. Discriminant

The discriminant is a value calculated from the coefficients of a quadratic equation and its value determines the nature of the roots of the quadratic equation.

1. If D > 0, there are two distinct real solutions.

2. If D = 0, there is one real solution (a repeated root).

3. If D < 0, there are no real solutions, but two complex conjugate solutions.

15. Pythagorean Theorem

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

• c is the hypotenuse (longest side across from the 90 degree angle).

• a and b are the other two sides.

16. The Equation of a Circle

The equation of a circle is a mathematical representation that describes all the points in a two-dimensional plane that are equidistant from a fixed point called the center.

• (x, y) is any point on the circle.

• (h, k) is the coordinates of the center of the circle.

• r is the radius of the circle.

17. Arc Length

Arc length refers to the length of a portion of the circumference of a circle or a curve. It is the distance along the curved line between two points on the arc.

• r is the radius of the circle.

• θ is the angle (in radians) subtended by the arc at the center.

18. Area of a Sector

The area of a sector is the region enclosed by an arc and the two radii originating from the center of a circle. It is a portion of the circle's total area.

• r is the radius of the circle.

• θ is the central angle of the sector (in radians).

19. Converting between Radians and Degrees

Converting between radians and degrees is a common operation in trigonometry and geometry.

20. Complementary Angle Relationship of Sine and Cosine

The complementary angle relationship of sine and cosine refers to the relationship between the sine and cosine functions of two angles that sum up to 90 degrees (or ​π/2 radians).

Specifically, if θ and ϕ are complementary angles, meaning θ + ϕ = 90, then the sine of one angle is equal to the cosine of the other angle, and vice versa.